Lattice Representations for Computability Theory
ثبت نشده
چکیده
منابع مشابه
Representations of measurable sets in computable measure theory
This article is a fundamental study in computable measure theory. We use the framework of TTE, the representation approach, where computability on an abstract set X is defined by representing its elements with concrete “names”, possibly countably infinite, over some alphabet Σ. As a basic computability structure we consider a computable measure on a computable σ-algebra. We introduce and compar...
متن کاملSpaces allowing Type-2 Complexity Theory revisited
The basic concept of Type-2 Theory of Effectivity (TTE) to define computability on topological spaces ¢. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 complexity theory on ...
متن کاملRepresentations of the real numbers and of the open subsets of the set of real numbers
In previous papers we have presented a unified Type 2 theory of computability and continuity and a theory of representations. In this paper the concepts developed so far are used for the foundation of a new kind of constructive analysis. Different standard representations of the real numbers are compared. It turns out that the crucial differences are of topological nature and that most of the r...
متن کاملClosed Sets and Operators thereon: Representations, Computability and Complexity
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such representations had been devised over the past decades, particularly regarding closed subsets of Euclidean space plus subclasses thereof (like compact subsets). In ...
متن کاملTo Jessica
Blanck, J., 1997: Computability on topological spaces by eeective domain representations. Our aim in this thesis is to study a uniform method to introduce computability on large, usually uncountable, mathematical structures. The method we choose is domain representations using Scott{Ershov domains. Domain theory is a theory of approximations and incorporates a natural computability theory. This...
متن کامل